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This question is incomplete, the complete question is;
Suppose u and v are functions of x that are differentiable at x=0
and that { u(0) = 7, u'(0) = -5 } { v(0)= -1, v'(0) = -4 }
Find the values of the following derivatives at x = 0.
a) ( uv )
b) (
)
c) (
)
Answer:
a) ( uv ) = -23
b) (
) = 33
c) (
) = -32/49 or - 0.6531
Step-by-step explanation:
Given that;
{ u(0) = 7, u'(0) = -5 } { v(0)= -1, v'(0) = -4 }
a)
( uv )
we differentiate
( uv ) = uv' + vu'
at x = (0), we substitute our values
( uv ) = ( 7 × -4 ) + ( -1 × -5)
( uv ) = -28 + 5
( uv ) = -23
b)
(
)
we differentiate
(
) = ( vu' - uv' ) / v²
at x=0, we substitute our values
(
) = ( (-1 × -5) - (7 × -4 ) ) / (-1)²
(
) = (( 5 - ( -28 )) / 1
(
) = 33 / 1
(
) = 33
c) (
)
we differentiate
(
) = ( uv' - vu' ) / u²
at x=0, we substitute our values
(
) = ( (7 × -4) - (-1 × -4) ) / (7)²
(
) = ( -28 - ( 4 ) ) / 49
(
) = ( -28 - 4 ) /49
(
) = -32 / 49
(
) = -32/49 or - 0.6531